After entering your email address, a confirmation email will be sent to your inbox. Please approve this email to receive our weekly eBook update. We will not share your personal information with any third party.

About the book

Reviews

Shivkumar Hegde
★★★★☆

7 October 2012

This book sufficient knowledge for the learning aspects.Easy methods have been adopted for every conceptual theories.

Description

This textbook covers topics such as functions, single variable calculus, multivariate calculus, differential equations and complex functions. The necessary linear algebra for multivariate calculus is also outlined. More advanced topics which have been omitted, but which you will certainly come across, are partial differential equations, Fourier transforms and Laplace transforms.

Preface

This book is partly based on lectures I gave at NUI Galway and Trinity College Dublin between 1998 and 2000. It is by no means a comprehensive guide to all the mathematics an engineer might encounter during the course of his or her degree. The aim is more to highlight and explain some areas commonly found difficult, such as calculus, and to ease the transition from school level to university level mathematics, where sometimes the subject matter is similar, but the emphasis is usually different. The early sections on functions and single variable calculus are in this spirit. The later sections on multivariate calculus, differential equations and complex functions are more typically found on a first or second year undergraduate course, depending upon the university. The necessary linear algebra for multivariate calculus is also outlined. More advanced topics which have been omitted, but which you will certainly come across, are partial differential equations, Fourier transforms and Laplace transforms.

This short text aims to be somewhere first to look to refresh your algebraic techniques and remind you of some of the principles behind them. I have had to omit many topics and it is unlikely that it will cover everything in your course. I have tried to make it as clean and uncomplicated as possible.

Hopefully there are not too many mistakes in it, but if you find any, have suggestions to improve the book or feel that I have not covered something which should be included please send an email to me at batty.mathmo (at) googlemail.com

Michael Batty, Durham, 2010.

Content

Preliminaries

Number Systems: The Integers, Rationals and Reals

Working with the Real Numbers

Complex Numbers

Vectors and Matrices

Vectors

Matrices and Determinants

Systems of Linear Equations and Row Reduction

Bases

Eigenvalues and Eigenvectors

Functions and Limits

Functions

Limits

Continuity

Calculus of One Variable Part 1: Differentiation

Derivatives

The Chain Rule

Some Standard Derivatives

Dierentiating Inverse Functions

Implicit Differentiation

Logarithmic Differentiation

Higher Derivatives

L’Hôpital’s Rule

Taylor Series

Calculus of One Variable Part 2: Integration

Summing Series

Integrals

Antiderivatives

Integration by Substitution

Partial Fractions

Integration by Parts

Reduction Formulae

Improper Integrals

Calculus of Many Variables

Surfaces and Partial Derivatives

Scalar Fields

Vector Fields

Jacobians and the Chain Rule

Line Integrals

Surface and Volume Integrals

Ordinary Differential Equations

First Order Dierential Equations Solvable by Integrating Factor

First Order Separable Differential Equations

Second Order Linear Differential Equations with Constant Coefficients: The Homogeneous Case

Second Order Linear Differential Equations with Constant Coefficients: The Inhomogeneous Case

Initial Value Problems

Complex Function Theory

Standard Complex Functions

The Cauchy-Riemann Equations

Complex Integrals

Index

This website uses cookies to improve user experience. By using our website you consent to all cookies in accordance with EU regulation.